HLLC-type methods for compressible two-phase flow in ducts with discontinuous area changes

Abstract

In this work, the Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver is extended to two-phase flow through ducts with discontinuous cross-sections. Two main strategies are explored regarding the treatment of the non-conservative term arising in the governing equations. In the first, labelled HLLC+S, the non-conservative term is discretized separately. In the second, labelled HLLCS, the non-conservative term is incorporated in the Riemann solver. The methods are assessed by numerical tests for single and two-phase flow of CO2, the latter employing a homogeneous equilibrium model where the thermodynamic properties are calculated using the Peng–Robinson equation of state. The methods have different strengths, but in general, HLLCS is found to work best. In particular, it is demonstrated to be equally accurate and more robust than existing methods for non-resonant flow. It is also well-balanced for subsonic flow in the sense that it conserves steady-state flow.